If you want the quilt to be washable, you have to take the ties apart and take the stabilizer out of them. The stabilizer will shrink and distort unpredictably if left in.
Someone on the QB says she washes the ties in a bag in the machine first (keep like colors together), then takes them apart, then backs them with Pellon SF101 Shape Flex Woven Fusible . I bought some of the fusible on eBay to try out, but have several tops to finish before I get the ties out.